Spatial AnalysisWhat is it? • “…the purpose of geographic inquiry is to examine relationships between geographic features collectively and to use the relationships to describe the real-world phenomena that map features represent.” (Clarke 2001, 182). • One Definition: the quantitative procedures employed in the study of the spatial arrangement of features (points, lines, polygons and surfaces)
Geographic Information Analysis • “Geographic information analysis is…concerned with investigating the patterns that arise as a result of processes that may be operating in space” (p. 3). • “Techniques [that] enable the representation, description, measurement, comparison, and generation of spatial patterns…”
How Do We Represent the World (in Map or Digital Form?) • Raster – Vector • A Higher Level of Abstraction? (p. 5) • Objects and Fields • The key distinction (according to your authors) • A slightly different conceptualization • How do we choose the “best” representation(s)?
Spatial Analysis:What is it? • What types of relationships exist between geographic features, and how do we express them? • Properties of spatial features and/or relationships between them: size, distribution, pattern, contiguity, neighborhood, shape, scale, orientation
3 Fundamental Questions Regarding Spatial Relationships • How can two (or more) spatial distributions be compared with each other? • How can variations in geographic properties over a single area or data set be described and/or analyzed? • How can we use what we have learned from an analysis(es) to predict future spatial distributions? Spatial Analysis can cover the spectrum implied by these questions!
What role does GIS play in Spatial Analysis? • GIS is a tool with unique capabilities: • Can handle geographically-referenced data • Spatial/attribute data entry/update capabilities • Data conversion functions • Storage and organization of a variety of spatial and attribute data • Manipulation of spatial and attribute data (encompasses many different operations) • Presentation/display capabilities • Spatial analysis tools (many tools may be used in combination)
Do you remember the 5 functional elements of a GIS? • Data acquisition • Preprocessing • Database Management • Manipulation/Analysis • Final product output These elements are all part of the spatial analysis “equation” (and a GIS professional’s knowledge base).
Our framework this semester for discussing GIS operations/procedures that are useful for spatial analysis… • The Pitfalls and Potential of Spatial Data • Maps as Outcomes of Processes • Point Pattern Analysis • Describing and Analyzing Fields • Statistical Analysis of Fields/Spatial Interpolation • Map Overlay Concepts and Procedures • Spatial Modeling • Network Analysis
How can we characterize Spatial Analysis (what skills does it require)? • Spatial analysis is an artistic and a scientific endeavor (what does this mean?) • It requires knowledge of the problem and/or question to be answered • It requires knowledge about the data (how it was collected, organized, coded, etc.) • It requires knowledge of GIS capabilities • It may require knowledge of statistical techniques • It requires envisioning the results of any operation…and the combination of any operations • It is not completely objective, in fact some argue that it is completely subjective • Many times there is more than one way to derive information that answers a question
Are Spatial Data “Special,” and if They Are, Why? • Spatial Data are Special… • Why? • How? • What are the implications? • Pitfalls • Potential • Why “They” Need “Us”
The “Pitfalls” of Spatial Data • Most spatial samples are not random!! • This situation/problem is known as spatial autocorrelation • The earth’s surface is not an isotropic plane • Positive autocorrelation, negative auto correlation, zero autocorrelation • “…Describing the autocorrelation structure, is of primary importance in spatial analysis.” (p. 29) • First order, and second order spatial variation
The “Pitfalls” of Spatial Data • The Modifiable Areal Unit Problem • “…aggregation units used are arbitrary with respect to the phenomena under investigation” • “If spatial units…were specified differently, we might observe very different patterns…” (p. 30) • The Ecological Fallacy • Rampant in media reporting
The “Pitfalls” of Spatial Data • Scale Issues • Examples • Nonuniformity of Space and Edge Effects • Space is not uniform • Edge Effects?
The Potential of Spatial Data • Quantification of Spatial Relationships • How? What kind of relationships matter? • Summarizing spatial relationships • How?
Spatial data are the building blocks of any spatial analysis • Spatial data structures: • Raster: geographically-referenced matrix of uniform size cells…advantages and disadvantages • Vector: features on the earth’s surface are represented as geographically-referenced vector objects (points, lines, polygons)…advantages and disadvantages
Representation of vector spatial objects • Hierarchical nature of objects (points, lines, polygons) • Points: different types • Entity, label, area, node • Lines: • Line, arc, link, etc. • Polygons: • Area, polygon, complex polygon
Basic elements of spatial information required to undertake spatial analysis • Location • X,Y coordinate or locational reference • Attribute data • Describing the (aspatial) characteristics of locations • Topology • Describing the spatial relationships between spatial features
Measurement of Location: GIS Issues • A GIS suitable for spatial analysis must have the necessary functions dealing with coordinate systems • What are these functions? • What coordinate systems do we normally see or work with in a GIS…and what are their characteristics?
Measurement of Location: GIS Issues • Basic measurement of spatial features: • Points are defined by x,y coordinates • Lines are represented by an ordered sequence of points…they can be “decomposed” into sections of straight line segments • The distance between two points on a Cartesian plane is derived through Euclidean distance…the length of a line segment is the sum total of the Euclidean distances of all segments that compose it (p. 105 Chou) • The area of any feature represented as a polygon an be computed by constructing a trapezoid from every line segment delineating the polygon…then systematically aggregating the trapezoid areas (both positive and negative) (p. 106 Chou)
Attribute Data Measurement • Categories: Nominal and Ordinal data • Numeric: Interval and ratio data • Measures of Central Tendency (mode, median, mean) and Dispersion (variance, standard deviation) • Must be cognizant of spatial units and geographic sampling techniques
Topology: What kinds of spatial relationships between spatial features? • Adjacency: Which polygons are adjacent to which? Often used in the spatial analysis of areal data. • Containment: Which spatial features are contained within which? Can be used for selection or perhaps geocoding. • Connectivity: Which line segments are connected? Often used for network analysis.
The Arc-node Data Model: a method of expressing vector topology • Used for ARC/INFO coverages (we will use this as our example)…a proprietary ESRI vector spatial data structure • Topological data is stored in “attribute tables”: point attribute tables (PATs), arc attribute tables (AATs), polygon attribute tables (PATs)…what is contained in these tables?
Sample Attribute Tables • Arc Attribute Tables (AATs) - contain the following data fields: arc-ID, Length, F-node, T-node, L-poly, R-poly • Polygon Attribute Tables (PATs) – contain the following data fields: poly-ID, perimeter, area • Point Attribute Tables (PATs) – the same fields as above, but zero perimeter and area ** These tables store the topological data needed to quantify the spatial relationships between features
Spatial Data Formats • Spatial data formats are the product of the private sector working to create data files that allow users to: • Create maps • Manipulate spatial data • Perform spatial analysis • Example ESRI spatial data formats (files): shapefiles, coverages, GRIDs, geodatabases, TINs, Routes
3 Major vector-based datasets used in ArcGIS: Shapefiles, Coverages, Geodatabases • ESRI Shapefiles: • Spatial data is stored in binary files • Attribute data is stored in dBase tables • Contain one simple feature class • No topology is developed for spatial features • Types of shapefiles: point, line, polygon and multi-point
3 Major vector-based datasets used in ArcGIS: Shapefiles, Coverages, Geodatabases • ESRI ARC/INFO Coverages: • Spatial data is stored in binary files • Topological and attribute tables are stored in INFO tables • Contain topological features classes that define line or polygon topology • Topology is “built” for lines and polygons - lines: arcs, nodes and routes; polygons: arcs, label points, polygons, regions • Primary coverage feature classes are: point, arc, polygon, and node; secondary: tic, link, annotation; compound: region, route
ARC/INFO Coverages • ARC coverage files: defined by header files, index files, ARC, PAL, LAB, CNT, PRJ, LOG, TOL • ARC: arc definitions and vertices; PAL: contains polygon definitions; LAB: contains label point records; CNT: contains polygon centroid information; PRJ: contains projection information; TOL: contains the tolerance values to use when processing a polygon coverage
ESRI GRID file • ESRI’s proprietary raster file structure • Readable in ArcGIS without any extensions • The Spatial Analyst extension needed to perform analysis on these files • Follow conventions we have learned about: • Uniform raster cell size • Single value per cell • Continuous data (including null values)
“Special” Spatial Data Structures: TINs and Routes • Triangulated Irregular Networks (TINs): sample points are connected to form triangles, with the relief inside each represented as a plane or facet • VIPs (Very Important Points) • Delaunay Triangulation • 3-dimensional surface description • ArcGIS can generate these through the 3-D Analyst extension
“Special” Spatial Data Structures: TINs and Routes • Routes are spatial data structures generated to represent linear features • Used when the definition of linear features does not meet the needs of a network-based application • Dynamic segmentation procedure • New line segments are defined… • Based on the location of “events” • Measurements of offsets on segments • Network Analyst and ARC/INFO
3 Major vector-based datasets used in ArcGIS: Shapefiles, Coverages, Geodatabases • ESRI Geodatabase • All spatial, topological, and attribute data is stored in tables in a relational database • A feature dataset in a geodatabase can contain simple or topological feature classes • Many feature classes can be associated with a topological role within the geodatabase • User-defined associations can be created between features in different feature classes • Types of feature classes: point, line, polygon, annotation, simple junction, complex junction, simple edge, complex edge
The Geodatabase Data Model: “…a better way to associate behavior with [spatial] features was needed” • An object-oriented data model: data “objects” can have rules, relationships, topology • Facilitates the creation of “smart features” that are more complex than generic points, lines, or polygons • All data is stored in a relational database ( as opposed to separate spatial and attribute data)
Centralized management of data • Geodatabases organize data into a hierarchy of data objects: object classes, feature classes, feature datasets • Object class: a table in a geodatabase that stores non-spatial data • Feature class: a collection of features with the same type of geometry and the same attributes • Feature dataset: a collection of feature classes that have the same spatial reference system • “Simple” feature classes can exist either within or outside a feature dataset; topological feature classes must be contained within a feature dataset
Maps as Outcomes of Processes • [Spatial] patterns provide clues to a possible causal [spatial] process(es) • “…Usefulness of maps…remains in their inherent ability to suggest patterns in the phenomena they represent.” p. 52 • Conceptualizing spatial analysis as processes and patterns
Types of Processes: Spatial Processes and their Possible Realizations • Could the pattern we observe have been generated by this particular process? • Deterministic processes: • Processes whose outcome can be predicted exactly from knowledge of initial conditions • Many times can be mathematically described • Outcome always the same • Stochastic processes: • Processes whose outcome is subject to variation that cannot be given precisely by a mathematical formula • Introduction of a random (stochastic) element to model the range of potential solutions • “Chance process with well-defined mechanisms” p. 58
Predicting Patterns: Expected Results • Assumptions • Example: independent random process (IRP) (or complete spatial randomness (CSR)) • Math used to predict frequency distribution under assumed randomness • Observed vs. expected • What is this assumption called in the scientific method? • Real World – usually not characterized by spatial randomness • First-order effects: the earth is not an isotropic plane, and therefore some areas will be more attractive of phenomena than others • Second-order effects: the assumption that events are independent of each other is not realistic…i.e. the location of events will influence the location of other events
Point Pattern Analysis • The spatial properties of the entire set of points is analyzed (rather than individual points) • Requirements/Assumptions according to O’Sullivan and Unwin (pp.78-79)? • Descriptive statistics for point distributions • Frequency; density; geometric center; spatial dispersion; spatial arrangement
Point Pattern Analysis • Thinking about point patterns… • How can we describe and analyze them • The geographical properties of a point pattern are characterized (described) by geometric center and dispersion • Geometric (mean) center = mean x,y coordinates; dispersion = standard distance of x and y distribution • Geometric (mean) center is not a reliable measure of central tendency when either the x or y standard distance is large • What are these measures useful for?
Point Pattern Analysis • Density-based and distance-based measures • i.e. Point Density and Point Separation • Density: ratio of frequency to area…intensity of a pattern • depending on distribution within a defined study area may be misleading (pp. 81-82) • Quadrat Count Methods • Census or random methods • Issues?
Density-based measures • Quadrat Analysis – based on the frequency of occurrence of points within quadrat units • Requires overlaying quadrats onto a layer of point features • Once quadrats are overlayed onto the point layer, frequencies of points per quadrat can be counted • All quadrats are classified according to observed frequency of points • Null hypothesis: point features are randomly distributed
Density-based Measures • Kernel Density Estimation • A pattern has a density at any location… • Continous densities for defined “kernels” to create a continous surface
Distance-based Point Pattern Measures • The Logic of Distance Measures • Can be described using types (categories): • Clustered – points are concentrated in one or more groups/areas • Uniform – points are regularly spaced with relatively large interpoint distance • Random – Neither the clustered or uniform pattern is prevalent
Measuring Spatial Arrangement • Nearest Neighbor Analysis (Index) • Measures the degree of spatial dispersion in a point distribution based on minimizing interpoint distances • Logic: in general the average distance between points in a clustered pattern is less than in a uniform pattern\ • Logic: a random pattern is associated with an avg. interpoint distance larger than a clustered pattern but smaller than a uniform pattern • The “nearest neighbor” for each point feature must be determined, and the interpoint distance is computed
Measuring Spatial Arrangement • Nearest Neighbor Analysis (Index) con’t • Observed average nearest neighbor distances compared to expected average nearest distances assuming complete spatial randomness [CSR] (1/2 sq.rt. A/n) • NNI = Ad/Ed p.100 • NNI range: 0 to 2.1491…where 0 indicates perfectly clustered and 2.1491 indicates perfectly uniform (values close to 1 indicate a random pattern) • To test the statistical significance of an NNI value, a computed z value can be compared to a critical value (1.96)
Measuring Spatial Arrangement • Nearest Neighbor Analysis: Pros and Cons • Pros: relatively simple; easy to compute; straightforward logic • Cons: is not sensitive to complex patterns unless extended to include more than just nearest neighbors
The Concept of Spatial Autocorrelation • Spatial Autocorrelation: measures the extent to which the occurrence of one feature is influenced by the distribution of similar features in the adjacent area Why is this idea important in the context of “classical” statistical analysis? • Captures some aspects of point spatial distribution not reported by NNI or quadrat analysis • Spatial auto correlation is characterized as positive (the existence of one feature tends to attract similar features) or negative (the existence of one feature tends to deter the location of similar features)
Types of Area Objects • Natural Areas vs. Command Regions • Who cares? • Issues with Command Regions? • Raster • Pros and Cons? • Planar-enforced areas… • GIS-context?
Geometric Properties of Areas • Area • How is it calculated? • Shape • Comparison of a polygon to a known shape • Spatial pattern • Contact numbers • Fragmentation (FRAGSTATS)
Spatial Autocorrelation • Most common spatial autocorrelation statistic is Moran’s I coefficient • Similar to a traditional correlation coefficient • The I coefficient for the most part ranges between –1 and +1; larger negative values indicate a scattered pattern…positive values indicate a clustered pattern • Also Geary’s C (Geary’s Ratio) • The C coefficient tends to range between 0 and 2; values approaching 0 imply similar values of a variable tend to cluster (positive spatial autocorrelation)…values approaching 2 indicate that dissimilar values tend to cluster
Spatial Autocorrelation • Joins Count approach • Logic?